1. Field of the Invention
The present invention relates generally to computer-implemented methods of solving systems of linear inequalities as a generic linear inequalities solver, and more particularly to air traffic analysis and control using a system of linear inequalities.
2. Background
Air traffic analysis and control can be represented as a problem that includes numerous linear variables and constraints. A simple example is documented Niedringhaus, “Stream Option Manager (SOM): Automated Integration of Aircraft Separation, Merging, Stream Management, and Other Air Traffic Control Functions” IEEE Transactions on Systems, Man, and Cybernetics, Vol. 25, No. 9, September 1995. Variables include the horizontal and vertical positions of aircraft at future times. Constraints for each aircraft include miles-in-trail spacing, due to airspace sector boundaries, sector entry/exit guidelines, aircraft capabilities, and separation from other aircraft. The number of variables and constraints grows with the number of aircraft.
The runtime for conventional methods of solving systems of linear inequalities grows as the cube of the number of aircraft, which may make it impractical to use these methods for, say, the entire Continental US (CONUS) airspace.
Therefore, efficient and accurate methods and systems for solving large systems of linear equations are needed.